3.737 \(\int 3^{1+x^2} x \, dx\)

Optimal. Leaf size=15 \[ \frac {3^{x^2+1}}{2 \log (3)} \]

[Out]

1/2*3^(x^2+1)/ln(3)

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2209} \[ \frac {3^{x^2+1}}{2 \log (3)} \]

Antiderivative was successfully verified.

[In]

Int[3^(1 + x^2)*x,x]

[Out]

3^(1 + x^2)/(2*Log[3])

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {align*} \int 3^{1+x^2} x \, dx &=\frac {3^{1+x^2}}{2 \log (3)}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.80 \[ \frac {3^{x^2+1}}{\log (9)} \]

Antiderivative was successfully verified.

[In]

Integrate[3^(1 + x^2)*x,x]

[Out]

3^(1 + x^2)/Log[9]

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fricas [A]  time = 0.39, size = 13, normalized size = 0.87 \[ \frac {3^{x^{2} + 1}}{2 \, \log \relax (3)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3^(x^2+1)*x,x, algorithm="fricas")

[Out]

1/2*3^(x^2 + 1)/log(3)

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giac [A]  time = 0.21, size = 13, normalized size = 0.87 \[ \frac {3^{x^{2} + 1}}{2 \, \log \relax (3)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3^(x^2+1)*x,x, algorithm="giac")

[Out]

1/2*3^(x^2 + 1)/log(3)

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maple [A]  time = 0.03, size = 14, normalized size = 0.93 \[ \frac {3^{x^{2}+1}}{2 \ln \relax (3)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3^(x^2+1)*x,x)

[Out]

1/2*3^(x^2+1)/ln(3)

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maxima [A]  time = 0.49, size = 13, normalized size = 0.87 \[ \frac {3^{x^{2} + 1}}{2 \, \log \relax (3)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3^(x^2+1)*x,x, algorithm="maxima")

[Out]

1/2*3^(x^2 + 1)/log(3)

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mupad [B]  time = 3.50, size = 11, normalized size = 0.73 \[ \frac {3\,3^{x^2}}{2\,\ln \relax (3)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3^(x^2 + 1)*x,x)

[Out]

(3*3^(x^2))/(2*log(3))

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sympy [A]  time = 0.10, size = 10, normalized size = 0.67 \[ \frac {3^{x^{2} + 1}}{2 \log {\relax (3 )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3**(x**2+1)*x,x)

[Out]

3**(x**2 + 1)/(2*log(3))

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